A Distributed Computing Perspective of Unconditionally Secure Information Transmission in Russian Cards Problems

TL;DR

This paper applies distributed computing techniques to analyze secure information transmission in Russian cards problems, focusing on minimizing information leakage while ensuring communication between players.

Contribution

It introduces a novel perspective using coding theory, Johnson graphs, and additive number theory to analyze deterministic protocols for secure card-based communication.

Findings

Provides bounds on information needed for secure transmission

Characterizes protocols that prevent eavesdropper from learning any card

Connects distributed computing concepts with cryptographic security in card problems

Abstract

The problem of $A$ privately transmitting information to $B$ by a public announcement overheard by an eavesdropper $C$ is considered. To do so by a deterministic protocol, their inputs must be correlated. Dependent inputs are represented using a deck of cards. There is a publicly known signature $(a,b,c)$, where $n = a + b + c + r$, and $A$ gets $a$ cards, $B$ gets $b$ cards, and $C$ gets $c$ cards, out of the deck of $n$ cards. Using a deterministic protocol, $A$ decides its announcement based on her hand. Using techniques from coding theory, Johnson graphs, and additive number theory, a novel perspective inspired by distributed computing theory is provided, to analyze the amount of information that $A$ needs to send, while preventing $C$ from learning a single card of her hand. In one extreme, the generalized Russian cards problem, $B$ wants to learn all of $A$'s cards, and in the other, $B$ wishes to learn something about $A$'s hand.